TSTP Solution File: GEO171+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO171+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:35:13 EDT 2022
% Result : Theorem 0.07s 0.29s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GEO171+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.07/0.26 % Computer : n026.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Wed Aug 31 06:57:51 EDT 2022
% 0.07/0.26 % CPUTime :
% 0.07/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.07/0.26 Usage: tptp [options] [-file:]file
% 0.07/0.26 -h, -? prints this message.
% 0.07/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.07/0.26 -m, -model generate model.
% 0.07/0.26 -p, -proof generate proof.
% 0.07/0.26 -c, -core generate unsat core of named formulas.
% 0.07/0.26 -st, -statistics display statistics.
% 0.07/0.26 -t:timeout set timeout (in second).
% 0.07/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.07/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.07/0.26 -<param>:<value> configuration parameter and value.
% 0.07/0.26 -o:<output-file> file to place output in.
% 0.07/0.29 % SZS status Theorem
% 0.07/0.29 % SZS output start Proof
% 0.07/0.29 tff(convergent_lines_type, type, (
% 0.07/0.29 convergent_lines: ( $i * $i ) > $o)).
% 0.07/0.29 tff(tptp_fun_Y_0_type, type, (
% 0.07/0.29 tptp_fun_Y_0: $i)).
% 0.07/0.29 tff(tptp_fun_X_1_type, type, (
% 0.07/0.29 tptp_fun_X_1: $i)).
% 0.07/0.29 tff(distinct_lines_type, type, (
% 0.07/0.29 distinct_lines: ( $i * $i ) > $o)).
% 0.07/0.29 tff(1,assumption,(~convergent_lines(Y!0, Y!0)), introduced(assumption)).
% 0.07/0.29 tff(2,assumption,(convergent_lines(X!1, X!1)), introduced(assumption)).
% 0.07/0.29 tff(3,plain,
% 0.07/0.29 (^[X: $i] : refl((~convergent_lines(X, X)) <=> (~convergent_lines(X, X)))),
% 0.07/0.29 inference(bind,[status(th)],[])).
% 0.07/0.29 tff(4,plain,
% 0.07/0.29 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.07/0.29 inference(quant_intro,[status(thm)],[3])).
% 0.07/0.29 tff(5,plain,
% 0.07/0.29 (![X: $i] : (~convergent_lines(X, X)) <=> ![X: $i] : (~convergent_lines(X, X))),
% 0.07/0.29 inference(rewrite,[status(thm)],[])).
% 0.07/0.29 tff(6,axiom,(![X: $i] : (~convergent_lines(X, X))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','apart3')).
% 0.07/0.29 tff(7,plain,
% 0.07/0.29 (![X: $i] : (~convergent_lines(X, X))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.07/0.29 tff(8,plain,(
% 0.07/0.29 ![X: $i] : (~convergent_lines(X, X))),
% 0.07/0.29 inference(skolemize,[status(sab)],[7])).
% 0.07/0.29 tff(9,plain,
% 0.07/0.29 (![X: $i] : (~convergent_lines(X, X))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.07/0.29 tff(10,plain,
% 0.07/0.29 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(X!1, X!1))),
% 0.07/0.29 inference(quant_inst,[status(thm)],[])).
% 0.07/0.29 tff(11,plain,
% 0.07/0.29 ($false),
% 0.07/0.29 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.07/0.29 tff(12,plain,(~convergent_lines(X!1, X!1)), inference(lemma,lemma(discharge,[]))).
% 0.07/0.29 tff(13,plain,
% 0.07/0.29 ((~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))) <=> (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.07/0.29 inference(rewrite,[status(thm)],[])).
% 0.07/0.29 tff(14,plain,
% 0.07/0.29 ((~![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))) <=> (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y)))),
% 0.07/0.29 inference(rewrite,[status(thm)],[])).
% 0.07/0.29 tff(15,axiom,(~![X: $i, Y: $i] : (convergent_lines(X, Y) => distinct_lines(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','con')).
% 0.07/0.29 tff(16,plain,
% 0.07/0.29 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.07/0.29 tff(17,plain,
% 0.07/0.29 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[16, 13])).
% 0.07/0.29 tff(18,plain,
% 0.07/0.29 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.07/0.29 tff(19,plain,
% 0.07/0.29 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[18, 13])).
% 0.07/0.29 tff(20,plain,
% 0.07/0.29 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.07/0.29 tff(21,plain,
% 0.07/0.29 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.07/0.29 tff(22,plain,
% 0.07/0.29 (~![X: $i, Y: $i] : ((~convergent_lines(X, Y)) | distinct_lines(X, Y))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[21, 13])).
% 0.07/0.29 tff(23,plain,(
% 0.07/0.29 ~((~convergent_lines(X!1, Y!0)) | distinct_lines(X!1, Y!0))),
% 0.07/0.29 inference(skolemize,[status(sab)],[22])).
% 0.07/0.29 tff(24,plain,
% 0.07/0.29 (convergent_lines(X!1, Y!0)),
% 0.07/0.29 inference(or_elim,[status(thm)],[23])).
% 0.07/0.29 tff(25,plain,
% 0.07/0.29 (^[X: $i, Y: $i, Z: $i] : refl((convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.07/0.29 inference(bind,[status(th)],[])).
% 0.07/0.29 tff(26,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(quant_intro,[status(thm)],[25])).
% 0.07/0.29 tff(27,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(rewrite,[status(thm)],[])).
% 0.07/0.29 tff(28,plain,
% 0.07/0.29 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((convergent_lines(X, Z) | convergent_lines(Y, Z)) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (convergent_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.07/0.29 inference(bind,[status(th)],[])).
% 0.07/0.29 tff(29,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z))) <=> ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(quant_intro,[status(thm)],[28])).
% 0.07/0.29 tff(30,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (convergent_lines(X, Z) | convergent_lines(Y, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ax6')).
% 0.07/0.29 tff(31,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.07/0.29 tff(32,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.07/0.29 tff(33,plain,(
% 0.07/0.29 ![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(skolemize,[status(sab)],[32])).
% 0.07/0.29 tff(34,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.07/0.29 tff(35,plain,
% 0.07/0.29 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.07/0.29 inference(rewrite,[status(thm)],[])).
% 0.07/0.29 tff(36,plain,
% 0.07/0.29 ((convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0))) <=> ((~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.07/0.29 inference(rewrite,[status(thm)],[])).
% 0.07/0.29 tff(37,plain,
% 0.07/0.29 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | ((~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)))),
% 0.07/0.29 inference(monotonicity,[status(thm)],[36])).
% 0.07/0.29 tff(38,plain,
% 0.07/0.29 (((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))) <=> ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1))),
% 0.07/0.29 inference(transitivity,[status(thm)],[37, 35])).
% 0.07/0.29 tff(39,plain,
% 0.07/0.29 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1) | (~convergent_lines(X!1, Y!0)))),
% 0.07/0.29 inference(quant_inst,[status(thm)],[])).
% 0.07/0.29 tff(40,plain,
% 0.07/0.29 ((~![X: $i, Y: $i, Z: $i] : (convergent_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (~convergent_lines(X!1, Y!0)) | convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.07/0.29 tff(41,plain,
% 0.07/0.29 (convergent_lines(Y!0, X!1) | convergent_lines(X!1, X!1)),
% 0.07/0.29 inference(unit_resolution,[status(thm)],[40, 34, 24])).
% 0.07/0.29 tff(42,plain,
% 0.07/0.29 (convergent_lines(Y!0, X!1)),
% 0.07/0.29 inference(unit_resolution,[status(thm)],[41, 12])).
% 0.07/0.29 tff(43,plain,
% 0.07/0.29 (~distinct_lines(X!1, Y!0)),
% 0.07/0.29 inference(or_elim,[status(thm)],[23])).
% 0.07/0.29 tff(44,plain,
% 0.07/0.29 (^[X: $i, Y: $i, Z: $i] : refl((distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))))),
% 0.07/0.29 inference(bind,[status(th)],[])).
% 0.07/0.29 tff(45,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(quant_intro,[status(thm)],[44])).
% 0.07/0.29 tff(46,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(rewrite,[status(thm)],[])).
% 0.07/0.29 tff(47,plain,
% 0.07/0.29 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(rewrite((distinct_lines(Y, Z) | convergent_lines(X, Z)) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))))), rewrite((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))), ((convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))))),
% 0.07/0.29 inference(bind,[status(th)],[])).
% 0.07/0.29 tff(48,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(quant_intro,[status(thm)],[47])).
% 0.07/0.29 tff(49,axiom,(![X: $i, Y: $i, Z: $i] : (convergent_lines(X, Y) => (distinct_lines(Y, Z) | convergent_lines(X, Z)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax','ceq3')).
% 0.07/0.29 tff(50,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.07/0.29 tff(51,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.07/0.29 tff(52,plain,(
% 0.07/0.29 ![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(skolemize,[status(sab)],[51])).
% 0.07/0.29 tff(53,plain,
% 0.07/0.29 (![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.07/0.29 tff(54,plain,
% 0.07/0.29 (((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!1, Y!0) | convergent_lines(Y!0, Y!0) | (~convergent_lines(Y!0, X!1)))) <=> ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(X!1, Y!0) | convergent_lines(Y!0, Y!0) | (~convergent_lines(Y!0, X!1)))),
% 0.07/0.29 inference(rewrite,[status(thm)],[])).
% 0.07/0.29 tff(55,plain,
% 0.07/0.29 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | (distinct_lines(X!1, Y!0) | convergent_lines(Y!0, Y!0) | (~convergent_lines(Y!0, X!1)))),
% 0.07/0.29 inference(quant_inst,[status(thm)],[])).
% 0.07/0.29 tff(56,plain,
% 0.07/0.29 ((~![X: $i, Y: $i, Z: $i] : (distinct_lines(Y, Z) | convergent_lines(X, Z) | (~convergent_lines(X, Y)))) | distinct_lines(X!1, Y!0) | convergent_lines(Y!0, Y!0) | (~convergent_lines(Y!0, X!1))),
% 0.07/0.29 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.07/0.29 tff(57,plain,
% 0.07/0.29 ($false),
% 0.07/0.29 inference(unit_resolution,[status(thm)],[56, 53, 43, 42, 1])).
% 0.07/0.30 tff(58,plain,(convergent_lines(Y!0, Y!0)), inference(lemma,lemma(discharge,[]))).
% 0.07/0.30 tff(59,plain,
% 0.07/0.30 ((~![X: $i] : (~convergent_lines(X, X))) | (~convergent_lines(Y!0, Y!0))),
% 0.07/0.30 inference(quant_inst,[status(thm)],[])).
% 0.07/0.30 tff(60,plain,
% 0.07/0.30 ($false),
% 0.07/0.30 inference(unit_resolution,[status(thm)],[59, 9, 58])).
% 0.07/0.30 % SZS output end Proof
%------------------------------------------------------------------------------